Superconvergence Results for Weakly Singular Fredholm-Hammerstein Integral Equations

In this article, we consider the multi-Galerkin method for solving the Fredholm-Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence for the algebraic kernel, whereas for logarithmic kernel, it conv...

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Bibliographic Details
Published in:Numerical functional analysis and optimization Vol. 40; no. 5; pp. 548 - 570
Main Authors: Mandal, Moumita, Nelakanti, Gnaneshwar
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.04.2019
Taylor & Francis Ltd
Subjects:
Algebra
Convergence
Formulas (mathematics)
Fredholm-Hammerstein integral equations
Galerkin method
Integral equations
Kernels
Mathematical analysis
multi-Galerkin method
piecewise polynomial
Polynomials
Smoothness
superconvergence rates
weakly singular kernels
ISSN:0163-0563, 1532-2467
Online Access:Get full text
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Summary:In this article, we consider the multi-Galerkin method for solving the Fredholm-Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence for the algebraic kernel, whereas for logarithmic kernel, it converges with the order in uniform norm, where h is the norm of the partition and r is the smoothness of the solution. We also discuss the iterated multi-Galerkin method. We prove that iterated multi-Galerkin method has order of convergence for the algebraic kernel and for logarithmic kernel, it has order of convergence of order in uniform norm. Numerical examples are given to illustrate the theoretical results.
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1561468